The mechanical properties of braided carbon nanotube yarns (CNTYs) on an elastomeric core to produce stretchable conductive materials were modeled and studied under tension. The elastomeric core served as the stretchable spring and the CNTYs braiding, with shape changing capabilities, as the conductive shell. The model predicts the stress-strain behavior of the composite as a function of the initial braiding angle and the number of pitches. The innovative aspect was included in the model related to the friction between the braid and the core. Results indicated good agreement between the theoretical model and the experimental results. Since the rate of the diameter decrease of the CNTYs braid was higher than that of the elastomeric core diameter, squeezing out of the core through the braid inter yarn space occurred. This limited the maximum potential extension of the braid. Thus, a critical strain was defined where the braid came into contact with the core. The addition of the friction stresses made a significant contribution to the overall stresses and the accuracy of the model and its agreement with the experimental results. An apparent friction coefficient was proposed to account for the effect of the elastomer core/braid interactive restriction and squeezing out of the elastomer through the braiding, as observed in experimental results. As the CNTYs are conductive, a stretchable conductive composite was obtained having a resistivity of 9.05x10-4 Ohm*cm, which remained constant throughout the tensile loading until failure and under cyclic loading.